Method of precision calibration of magnification of a scanning microscopes with the use of test diffraction grating

ABSTRACT

A method of precision calibration of magnification of scanning microscopes with the use of a test diffraction grating includes positioning and orientation of a test object on a stage of microscope so that strips of a test diffraction grating are perpendicular to a direction along which a calibration is performed, scanning of a selected portion of the test object along axes X and Y, measuring values of a signal S versus coordinates x and y in a plane of scanning and storing of the values S (x, y) in a digital form as a two-dimensional digital array, transforming the two-dimensional array of signals S(x, y) into a two-dimensional array S (u, v) by turning of the axes so that a direction of a new axis u is perpendicular to the strips of the grating and a direction of a new axis v coincides with the strips of the grating, line-by-line mathematical processing of the array S(u,v) for each line, converting of the one dimensional, complex function into a one-dimension spectrum of real values of a module, finding from the spectrum of the real values a greatest spectral maximum and determining its characteristic frequency as an abscissa of a point with the maximum value, calculating an average value of a pitch of the diffraction grating; performing the mathematical processing, the conversion, the determination and the calculation for subsequent lines with a new value of a coordinate v, statistically processing the thusly obtained values for all lines and determining an average value and a standard deviation over a whole frame, and determining a magnification M u  in accordance with the selected direction u.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to the methods of precisioncalibration of magnification of scanning microscopes with the use of atest diffraction grate.

[0002] Methods of precision calibration of a magnification of syntheticmicroscopes with the use of a test diffraction gratings are known. Inthe existing methods test object is positioned and oriented on amicroscope table, and corresponding part of the test objects is scanned,with subsequent processing of the thusly obtained data. It is believedthat the existing methods can be further improved.

SUMMARY OF THE INVENTION

[0003] Accordingly, it is an object of the present invention to providea method of precision calibration of magnification of a scanningmicroscopes with the use of a test diffraction grating.

[0004] In keeping with these objects and with others which will becomeapparent hereinafter, one feature of present invention resides, brieflystated, in a method of precision calibration of magnification ofscanning microscopes with the use of a test diffraction grating,comprising the steps of positioning and orientation of a test object ona table of microscope so that strips of a test diffraction grate areperpendicular to a direction along which a calibration is performed;scanning of a selected portion of the test object along axes X and Y;measuring values of a signal S versus coordinates X and Y in a plane ofscanning and storing of said values S (x, y) in a digital form as atwo-dimensional digital array; transforming the two-dimensional array ofsignals S(x, y) into a two-dimensional array S (u, v) by turning of theaxes so that a direction of a new axis u is perpendicular to the stripsof the grating and a direction of a new axis v coincides with the stripsof the grating; line-by-line mathematical processing of the array S(u,v)for each line S(u) by calculating of a Fourier spectrum of the lineSP(ω) in correspondence with the formula${{{SP}(\omega)} = {\frac{1}{\sqrt{2 -}}{\int_{- \infty}^{\infty}{{{S(u)} \cdot \exp}\quad ( {{iu}\quad \omega} )\quad {u}}}}},$

[0005] wherein ω is a coordinate in a reciprocal space which representsa space frequency; SP(ω) is a complex spectrum density which correspondsto the space frequency ω; S(u) is a function which describes aone-dimensional profile of the signal; and i={square root}−1 is animaginary unit; converting of the one dimensional complex function SP(ω) into a one-dimensional spectrum of real values of a module |SP(ω)|by multiplying of each value SP(ω) by a complex-conjugate value; findingfrom the spectrum of the real values T the greatest spectral maximum anddetermining its characteristic frequency ω_(h) as an abscissa of a pointwith the maximum value |SP|; calculating an average value of a pitchT_(h) of the diffraction grate in accordance with the formula:$T_{h} = \frac{1}{W_{h}}$

[0006] performing the mathematical processing, the conversion, thedetermination and the calculation for subsequent lines S(u) with a newvalue of a coordinate v; statistically processing the thusly obtainedset of values T_(h) for all lines and determining an average value T anda standard deviation ΔT over a whole frame; and determining amagnification M_(u) in accordance with the selected direction u inaccordance with the formula:${M_{u} = \frac{T \cdot L}{T_{0} \cdot N}},$

[0007] where L is a width of a medium of image in direction of thecalibration, T₀ is an independently obtained value of the pitch of thesame test object, and N is a number of pixels in the line along thedirection u.

[0008] When the method is performed in accordance with the presentinvention, it reliably provides a precision calibration of magnificationof scanning microscopes, and achieves a very high accuracy ofcalibration.

[0009] The novel features which are considered as characteristic for thepresent invention are set forth in particular in the appended claims.The invention itself, however, both as to its construction and itsmethod of operation, together with additional objects and advantagesthereof, will be best understood from the following description ofspecific embodiments when read in connection with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1 is a view showing an image of a test object with directionsof scanning and a direction in which a multiplication of a microscope isto be determined;

[0011]FIG. 2 is a view additionally illustrating a second coordinatesystem, in which an obtained array of signals is to be converted;

[0012]FIG. 3 is a view illustrating a transformed one dimensional arrayof signals in accordance with one line of azzay S(u,v); and

[0013]FIG. 4 is a view showing a Fourier spectrum of the mathematicallyprocessed array of FIG. 3.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] In accordance with the present invention a method for precisioncalibration of a magnification of a scanning microscope is performedwith a test diffraction grating. FIG. 1 shows a field of view 1 of ascanning microscope with a plurality of pixels 2 of a signal of scanningwith an image of a diffraction grating. The directions of scanning areidentified with X and Y and the scanning is performed in accordance withthese two perpendicular axes. A magnification of calibration thescanning electron microscope is performed in direction lower u. As canbe seen from this drawing, the test object is positioned and oriented onthe microscope so that the strips of the test diffraction grate areperpendicular to the direction u of calibration.

[0015] A portion of the test object which is shown in FIG. 1 is thenscanned, and a plurality of values of the signal S versus thecoordinates in a plane of scanning are obtained. These values areidentified as S(x, y) and they are stored in a digital form as atwo-dimensional digital array, for example in a memory of a computer.The thusly obtained two dimensional array of signals S(x, y) istransformed into a two dimensional array S(u, v) by turning of the axes,so that a direction of a new axis u is perpendicular to the strips ofthe grating, and a direction of a new axis v corresponds to thedirection of the strips of the grating, as shown in FIG. 2. Thereby anew array of the signal is obtained.

[0016] Then line-by-line mathematical processing of the array S(u,v) isperformed for each line S(u) by calculating of a Fourier spectrum of theline SP(ω) in correspondence with the formula${{{SP}(\omega)} = {\frac{1}{\sqrt{2 -}}{\int_{- \infty}^{\infty}{{{S(u)} \cdot \exp}\quad ( {{iu}\quad \omega} )\quad {u}}}}},$

[0017] wherein ω is a coordinate in a reciprocal space which representsa space frequency; SP(ω) is a complex spectrum density which correspondsto the space frequency ω; S(u) is a function which describesone-dimensional profile of a signal; and i={square root}−1 is animaginary unit. The one dimensional, complex function SP (ω) isconverted into a one-dimensional spectrum of real values of a module|SP(ω)| by multiplying of each value SP (ω) by a complex-conjugatevalue. From |SP(ω)| a greatest spectral maximum is then found, and acharacteristic frequency ω_(h) is determined as an abscissa of a pointwith the maximum value |SP|. An average value of a pitch T_(h) of thediffraction grating is calculated in accordance with the formula:$T_{h} = \frac{1}{W_{h}}$

[0018] Then there are performed a mathematical processing, a conversion,a determination and a calculation for subsequent lines S(u) with a newvalue of a coordinate v. The thusly obtained values T_(h) arestatistically processed, and for all lines an average value T and astandard deviation ΔT over a whole frame are determined. A magnificationM_(u) in accordance with the selected direction u is determined inaccordance with the formula:${M_{u} = \frac{T \cdot L}{T_{0} \cdot N}},$

[0019] where L is a width of a medium of image in direction of thecalibration, T₀ is an independently obtained value of the pitch of thetest object, and N is a number of pixels in the line along the directiony.

[0020] In accordance with the invention before the line-by-linemathematical processing a preliminary evaluating determination of apitch T¹ of the test object in its microscopic representation and anerror value δT¹; is determined. A characteristic frequency W_(h) ¹ andits error value Δω_(h) ¹ in accordance with the formulas$\omega_{h}^{1} = {{\frac{1}{T^{1}}\quad {and}\quad \Delta \quad \omega_{h}^{1}} = \frac{2\delta \quad T^{1}}{( T^{1} )^{2} - ( {\delta \quad T^{1}} )^{2}}}$

[0021] Then a function SP(ω) is calculated by said line-by-linemathematical processing in a limited band of frequencies from ω_(h)¹-Δω¹ to ω_(h) ¹+Δω_(h) ¹.

[0022] Furthermore, in the inventive method the greatest spectralmaximum can be determined by approximating of |SP(ω)| in a neighborhoodof the greatest maximum by a corresponding analytical curve, localizingon the analytical curve an extemum with an abscissa taken as thecharacteristic frequency ω_(h).

[0023] The finding of the greatest valued spectral maximum can beperformed by cutting off of a greatest spectral maximum in accordancewith a predetermined threshold, and forming an island of a spectralmaximum, calculating a centroid for said island, and fixating thecharacteristic frequency ω_(h) as an abscissa of the centroid.

[0024] In the inventive method before line-by-line mathematicalprocessing, suppressing of a noise can be performed.

[0025] It will be understood that each of the elements described above,or two or more together, may also find a useful application in othertypes of methods and constructions differing from the types describedabove.

[0026] While the invention has been illustrated and described asembodied in method of precision calibration of magnification of ascanning microscopes with the use of test diffraction grating, it is notintended to be limited to the details shown, since various modificationsand structural changes may be made without departing in any way from thespirit of the present invention.

[0027] Without further analysis, the foregoing will so fully reveal thegist of the present invention that others can, by applying currentknowledge, readily adapt it for various applications without omittingfeatures that, from the standpoint of prior art, fairly constituteessential characteristics of the generic or specific aspects of thisinvention.

[0028] What is claimed as new and desired to be protected by LettersPatent is set forth in the appended claims.

1. A method of precision calibration of magnification of a scanningmicroscope with the use of a test diffraction grating, comprising thesteps of positioning and orientation of a test object on stage ofmicroscope so that strips of a test diffraction grating areperpendicular to a direction along which a calibration is performed;scanning of a selected portion of the test object along axes X and Y;measuring values of a signal S versus on coordinates x and y in a planeof scanning and storing of said values S (x, y) in a digital form as atwo-dimensional digital array; transforming the two-dimensional array ofsignals S(x, y) into a two-dimensional array S (u, v) by turning of theaxes so that a direction of a new axis u is perpendicular to the stripsof the grate and a direction of a new axis v coincides with the stripsof the grate; line-by-line mathematical processing of the array S(u,v)for each line S(u) by calculating of a Fourier spectrum of the lineSP(ω) in correspondence with the formula${{{SP}(\omega)} = {\frac{1}{\sqrt{2 -}}{\int_{- \infty}^{\infty}{{{S(u)} \cdot \exp}\quad ( {{iu}\quad \omega} )\quad {u}}}}},$

wherein ω is a coordinate in a reciprocal space which represents a spacefrequency; SP (ω) is a complex spectrum density which corresponds to thespace frequency ω; S(u) is a function which describes a one-dimensionalprofile of a signal; and i={square root}−1 is an imaginary unit;converting of the one dimensional, complex function SP (ω) into aone-dimension spectrum of real values of a module |SP(ω)| by multiplyingof each value SP (ω) by a complex-conjugate value; finding from thespectrum of the real values T_(h) a greatest spectral maximum anddetermining its characteristic frequency ω_(h) as an abscissa of a pointwith the maximum value |SP|; calculating an average value of a pitchT_(h) of the diffraction grating in accordance with the formula:$T_{h} = \frac{1}{W_{h}}$

performing the mathematical processing, the conversion, thedetermination and the calculation for subsequent lines S(u) with a newvalue of a coordinate v; statistically processing the thusly obtainedset of values T_(h) for all lines and determining an average value T anda standard deviation ΔT over a whole frame; and determining amagnification M_(u) in accordance with the selected direction u inaccordance with the formula:${M_{u} = \frac{T \cdot L}{T_{0} \cdot N}},$

where L is a width of a medium of image in direction of the calibration,T₀ is an independently obtained value of the pitch of the test object,and N is a number of pixels in the line along the direction u.
 2. Amethod as defined in claim 1; and further comprising performing, beforethe line-by-line mathematical processing, a preliminary evaluatingdetermination of a pitch T¹ of the test object in its microscopicrepresentation and an error value ΔT¹; calculating of an evaluatingcharacteristic frequency ω_(h) ^(1′) and its error value Δω_(h) ¹ inaccordance with the formulas${\omega_{h}^{1} = {{\frac{1}{T^{1}}\quad {and}\quad {\Delta\omega}_{h}^{1}} = \frac{2\delta \quad T^{1}}{( T^{1} )^{2} - ( {\delta \quad T^{1}} )^{2}}}};$

and calculating of a function SP(ω) by said line-by-line mathematicalprocessing in a limited band of frequencies from ω_(h) ¹-Δω_(h) ¹ toω_(h) ¹+Δω_(h) ¹.
 3. A method as defined in claim 1, wherein finding ofthe greatest spectral maximum includes approximating of |SP(ω)| in aneighborhood of the greatest maximum by a corresponding analyticalcurve, localizing on the analytical curve an extremum with an abscissataken as the characteristic frequency ω_(h).
 4. A method as defined inclaim 1, wherein said finding of the greatest spectral maximum valueincludes cutting off of a greatest spectral maximum in accordance with apredetermined threshold and forming an island of a spectral maximum,calculating a centroid for said island, and fixating of thecharacteristic frequency ω_(h) as an absissa of the centroid.
 5. Amethod as defined in claim 1; and further comprising before line-by-linemathematical processing, suppressing of a noise.